a nondescript cat found everywhereThe originally-talkative tri-colored male cat had completely lost its voice, and established its status in our home as merely a pet. It had become a nondescript cat found everywhere – as if I had hallucinated that this cat had ever spoken in human language, now that I thought about it. The cat is great and not fastidious: its purrs are seldom, close to absent, as if it has forgotten cat language along with human language. Somehow it made my room its bed, and thus grew silent to the frequent dropping by of my sister, who is avid in taking care of Shamisen.
Tricolor male cats can't be "found anywhere," though Kyon may not realize it. Tricolor males are XXY, i.e. they have an extra chromosome. The tricolor pattern arises because the body of the cat is a mosaic of patches with one or the other X chromosome activated, with another gene that isn't on the X "whiting out" much of the coat.
I see ambiguous indications that characters in the story understand this point. I think it likely that that author understands. This is just a heads-up for translators.
is great and not fastidious This doesn't quite make sense. There's nothing "great" about a cat that isn't clean. "Not fussy" would seem closer to the point of an easy-going, tolerant cat.
thus grew silent This also doesn't quite make sense. Shami was never talkative about the sister, was he? So what sense does it make to say that he grew silent? Perhaps "thus is silent."
Alternatively, perhaps it's Kyon who is growing silent to his sister's intrusions.